Dynamic stability of a class of fractional-order nonlinear systems via fixed point theory

In this paper, the problem of the uniform stability for a class of fuzzy fractional-order genetic regulatory networks with random discrete delays, distributed delays, and parameter uncertainties is studied. Although there is a portion of literature on using fixed point theorems to study the stability of fractional neural networks, most of them required the fractional order to be in $\left(\frac{1}{2},1\right)$. However, the case of the fractional-order belonging to $(0,\frac{1}{2})$ has not been discussed. To solve it, this work proposes a novel idea of using fixed point theory to study the stability of fuzzy (0,1) order neural networks, the problem of the uniqueness of the solution of the considered genetic regulatory networks is resolved, and a novel sufficient condition to guarantee the uniform stability of above genetic regulatory networks is also derived. Eventually, an example is given to demonstrate that the obtained result is effective.     

A Generalization of Lappan’s Theorem to Higher Dimensional Complex Projective Space

In this paper, the authors discuss a generalization of Lappan’s theorem to higher dimensional complex projective space and get the following result: Let f be a holomorphic mapping of ? into Pⁿ(C), and let H₁, · · · , H_q be hyperplanes in general position in Pⁿ(C).Assume that sup {(1 ? |z|²)f^?(z) : z ∈ q[ j=1 f^?1(H_j )o < ∞,if q ≥ 2n² + 3, then f is normal.     

A Selective Cucurbit[8]uril-Peptide Beacon Ensemble for the Ratiometric Fluorescence Detection of Peptides

A convenient supramolecular strategy for constructing a ratiometric fluorescent chemosensing ensemble, consisting of a macrocyclic host (cucurbit[8]uril CB[8]), and a pyrene-tagged amphiphilic peptide beacon (AP 1), is reported. AP 1 unfolds upon encapsulation of the pyrene termini into the hydrophobic CB[8] cavity. This changes pyrene excimer to monomer emission. Substrates with higher affinity for the CB[8] cavity can displace AP 1 from the ensemble. The released AP 1 folds again to form a pyrene excimer, which allows for the ratiometric fluorescence monitoring of the substrate. In this report, the ensemble capacity for ratiometric fluorescence monitoring of biological substrates, such as amino acid derivatives, specific peptides, and proteins, in aqueous media is demonstrated.     

一类压缩型映射的不动点定理

在完备的度量空间中,讨论了一类新型的非线性压缩映射ρ(Tx,Ty)≤a(ρ(x,y))ρ(x,Tx)+b(ρ(x,y))ρ(y,Ty)+c(ρ(x,y))ρ(x,y)通过构造迭代序列,指出该映射的不动点的存在性和唯一性,并给出相应的误差估计式,拓展和改进了有关文献的范围.     

改进的PNC方法及其在非线性偏微分方程多解问题中的应用

2017年，李昭祥等提出了一种偏牛顿-校正法（Partial Newton-Correction Method，简记为PNC方法），并利用它成功地计算出了三类非线性偏微分方程的多重不稳定解.本文在PNC方法的基础上，提出并发展了一种改进的PNC方法.首先，利用Nehari流形$\mathcal{N}$与零平凡解的可分离性，建立并证明了$\mathcal{N}$的某特殊子流形$\mathcal{M}$上的全局分离定理及其推广（即局部分离定理）.全局分离定理只跟非线性偏微分算子或相应的非线性泛函本身有关，而与具体的计算方法无关.对一些典型的非线性偏微分方程多解问题（比如，Henon方程问题），该全局分离定理的分离条件，经验证是成立的.另一个方面，通过修改或补充原辅助变换的定义，去掉了原辅助变换的奇异性；接着建立并证明了某些非线性偏微分方程问题的新未知解与该非线性偏微分算子零核空间的密切关系；在证明中，去掉了在原奇异变换下所需的标准收敛（standard convergence）假设.最后，计算实例与数值结果验证了改进的PNC方法的可行性和有效性；同时表明子流形$\mathcal{M}$与已知解的可分离性是PNC方法和本文新方法能成功找到多解的关键.     

Cell–Membrane Penetration of Tat‐Conjugated Polymeric Micelles: Effect of Tat Coating Density

Considerable efforts have been devoted to enhancing the cell penetration of nanoparticles by coating cell‐penetrating peptides (CPPs) on the surface. However, the internalization mechanism for a CPP at different concentrations varies a lot. It is acknowledged that the mechanism is restricted to endocytic pathway at relatively low concentrations; however, direct translocation becomes dominant at high concentrations. This raises an interesting question on how the surface Tat coating density of the nanoparticles would influence their cell–membrane interaction and the consequent internalization behavior. This study systematically investigates the effect of Tat peptides on the internalization behavior of polymeric micelles by tuning surface Tat coating density, incubation concentrations, incubation time, and other factors using poly(ethylene glycol)–poly(ε‐caprolactone) copolymer (PEG‐PCL) micelles. It is found that both energy‐dependent and energy‐independent pathways are involved in the cellular uptake process, and the Tat‐conjugated polymeric micelles strongly accumulated on the cell surface at initial stage. The membrane‐anchoring and internalization rate increase with the increasing Tat coating density. Furthermore, the increasing of Tat coating density accelerates the energy‐independent pathway. It is envisioned that this finding will further shed light on the surface modification of nanoparticles for enhanced cell penetration and direct translocation into cell cytoplasm.     

Probing Adsorption Configurations of Small Molecules on Surfaces by Single-Molecule Tip-Enhanced Raman Spectroscopy

Determining the adsorption configurations of organic molecules on surfaces, especially for relatively small molecules, is a key issue for understanding the microscopic physical and chemical processes in surface science. In this work, we have applied low-temperature ultrahigh-vacuum tip-enhanced Raman scattering (TERS) technique to distinguish the configurations of small 4,4′-bipyridine (44BPY) molecules adsorbed on the Ag(111) surface. The observed Raman spectra exhibit notable differences in the spectral features which can be assigned to three different molecular orientations, each featuring a specific fingerprint pattern based on the TERS selection rule that determines the distribution of the relative intensities of different vibrational peaks. Furthermore, such a small molecule can in turn act as a local probe to provide information on the local electric field distribution at the tip apex. Our work showcases the capability of TERS technique for obtaining information on adsorption configurations of small molecules on surfaces down to the single-molecule level, which is of fundamental importance for many applications in the fields of molecular science and surface chemistry.     

Rapid,Traceless, AgI‐Promoted Macrocyclization of Peptides Possessing an N‐Terminal Thioamide

Peptide macrocyclization is often a slow process, plagued by epimerization and cyclodimerization. Herein, we describe a new method for peptide macrocyclization employing the Ag^I‐promoted transformation of peptide thioamides. The Ag^I has a dual function: chemoselectively activating the thioamide and tethering the N‐terminal thioamide to the C‐terminal carboxylate. Extrusion of Ag₂S generates an isoimide intermediate, which undergoes acyl transfer to generate the native cyclic peptide, resulting in a rapid, traceless macrocylization process. Cyclic peptides are furnished in high yields within 1 hour, free of epimerization and cyclodimerization.     

Regularized gap functions and error bounds for split mixed vector quasivariational inequality problems

In this paper, we consider a class of split mixed vector quasivariational inequality problems in real Hilbert spaces and establish new gap functions by using the method of the nonlinear scalarization function. Further, we obtain some error bounds for the underlying split mixed vector quasivariational inequality problems in terms of regularized gap functions. Finally, we give some examples to illustrate our results. The results obtained in this paper are new.